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henry is starting a t-shirt printing business and plans on selling each shirt for $30, with his cost being $8 per shirt. the equipment will cost $1200. henry orders 600 shirts and determines that the profit for his new business is modeled by the function p = 22x - 1200. what is the range of this function in this context
a) {0 ≤ x ≤ 500}
eliminate
b) {0 ≥ x ≥ 500}
c) {-1,200 ≤ p ≤ 2,000}
d) {-1,200 ≤ p ≤ 12,000}

Given the function, P = 22x - 1200, be the model determining the profit of Henry's new business. Now, the lowest amount that P could generate would be when Henry does not sell any shirt. This gives x a value of 0 and P = 0 - 1200 = -1200.

Now, he can get the highest profit when he gets to sell all of the 600 shirts. Thus, we have x = 600 and P = 22(600) - 1200 = 12000. 

Since the minimum and maximum values of P are -1200 and 12000, then the range of P would be {-1200 ≤ p ≤ 12000}.

D) {-1200 ≤ p ≤ 12000}

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